National City, one of the biggest mortgage lenders in the Midwest, was acquired in a rescue deal yesterday after months of speculation about whether the bank would survive at all.

PNC Financial Services said that it was buying National City for $5.58 billion (£3.5 billion) in a cash-and-shares deal, valuing the bank at a 19 per cent discount to its closing price on Thursday.

As a sweetener for the deal, PNC will also get $7.7 billion of capital from the US Treasury by selling a stake in the newly combined group to the American taxpayer.

The capital injection forms part of new legislation that allows the US Treasury to acquire shares in troubled banks to help them to survive the credit crisis.

On a conference call to Wall Street analysts yesterday, PNC said that it would have to write down $19.9billion of bad loans stagnating on National City's books. PNC refused to be drawn on whether it had been forced to buy National City by Henry Paulson, the US Treasury Secretary, as part of a move to secure the future of the lender. However, it sought to reassure shareholders by insisting that the new deal would create a larger and very well-capitalised bank.

At the end of 2006, National City had retail deposits of $87 billion. The bank, which is based in Columbus, Ohio, is heavily exposed to the housing crash in the Midwestern state, which has been one of those worst-affected by the American residential property slump. Ohio has suffered so badly because of the concentration of low-income mortgage borrowers who defaulted on monthly repayments.

National City shareholders will receive 0.0392 shares of PNC common stock for each share of National City they own. However, the discounted valuation of the lender comes after sharp declines to its share price over the past few months. This time last year, shares in National City were trading at around $24, but they fell to a little more than $1 this month. Rumours that the lender was facing funding difficulties dogged the share price and led the bank's chief executive to issue public reassurances about the health of the group.

It emerged yesterday that PNC had been mulling a takeover of National City for months. This week, National City posted a quarterly loss of $5.15 billion. The lender set aside $1.18 billion during the third quarter for loan-loss provisions, compared with provisions of $368 million during the same quarter a year earlier

Mr Paulson has been very active in forcing troubled banks to merge with other, better-capitalised groups. He has already overseen the acquisition of Washington Mutual by JPMorgan Chase and this month orchestrated the distressed break-up of Wachovia to Wells Fargo, the West Coast-based lender, and to Citigroup, the world's biggest bank.

The US Government is desperate for troubled banks to be taken over to avoid a withdrawal on the federal bank insurance fund, which guarantees up to $250,000 of Americans' savings. That fund is running dangerously low because around 15 banks have already gone bust in the United States this year alone.

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